RDFS-Plus
In Semantic Web RDFS-Plus is an extension of RDFS, and a subset of OWL
- even though the namespace is OWL, it’s considered as a subset
- Inference rules are shown with SPARQL CONSTRUCT queries
- for logical semantics behind there expressions see Semantic Web Logic
- DL-Lite something
Basic Constructs
owl:inverseOf: Inverse
Example
- suppose we have
:hasParent- then the inverse is:hasChild - the construction
owl:inverseOfmakes this relation explicit
In math,
- inverse of $f$ is $f^{-1}$:
- if $f(x) = y$, then $f^{-1}(y) = x$
- the same idea is in RDFS-Plus
```text only CONSTRUCT { ?y ?q ?x } WHERE { ?p owl:inverseOf ?q . ?x ?p ?y . }
Example:
- <code>lit:Shakespeare lit:wrote lit:Macbeth </code>
- we know that <code>lit:wrote owl:inverseOf lit:writtenBy</code>
- so, can infer that <code>lit:Macbeth lit:writtenBy lit:Shakespeare</code>
### <code>owl:SymmetricProperty</code>: Symmetric Properties
- in real life, a relation "married" is both-way:
- if $A$ is married on $B$, then $B$ is married on $A$
- suppose we have this assertion: <code>bio:Anne bio:married lit:Shakespeare</code>
- consider this query
- <code>SELECT ?who WHERE { ?lit:Shakespeare bio:married ?who }</code>
- it returns no answer| |- now state that married is both-way: it's inverse of itself | - <code>bio:married owl:inverseOf bio:married</code>
- now that query returns something
- this is an example of a <code>owl:SymmetricProperty</code>
- so instead of <code>owl:inverseOf</code> can say
- <code>bio:married rdf:type owl:SymmetricType</code>
```text only
CONSTRUCT { ?p owl:inverseOf ?p. }
WHERE { ?p a owl:SymmetricProperty . }
Also, can be useful to say that owl:inverseOf is symmetric
owl:inverseOf rdf:type owl:SymmetricProperty- now the following hold:
- $:P_1$
owl:inverseOf$:P_2 \Rightarrow$ - $:P_2$
owl:inverseOf$:P_1$
- $:P_1$
owl:TransitiveProperty: Transitivity
In math:
- $R$ is transitive if
- $a \ R \ b \land b \ R \ c \Rightarrow a \ R \ c$
In RDFS-plus, owl:TransitiveProperty is used for that:
:P rdf:type owl:TransitiveProperty
Meaning: ```text only CONSTRUCT { ?x ?p ?z .} WHERE { ?x ?p ?y . ?y ?p ?x . ?p a owl:TransitiveProperty . }
Note that for longer chains like $a \to b \to ... \to q$ the rule also holds
### <code>owl:equivalentClass</code>: Equivalence
Identity
- URIs give the global notion of identity
- but what if we merging two different sources that have the same concept, but under different URIs?
- i.e. we want to say that $:A \equiv :B$
- use [RDFS](RDFS):
- <code>:A rdfs:subClassOf :B</code> $\land$ <code>:B rdfs:subClassOf :A</code>
- semantically same effect is achieved with <code>owl:equivalentClass</code>
```carbon
CONSTRUCT { ?r rdf:type ?b .}
WHERE {
?a owl:equivalentClass ?b .
?r rdf:type ?a .
}
CONSTRUCT { ?r rdf:type ?a .}
WHERE {
?a owl:equivalentClass ?b .
?r rdf:type ?b .
}
Note that we need to have 2 CONSTRUCT statements
- because
owl:equivalentClassis symmetric - but instead of repeating twice can say that
owl:equivalentClass rdf:type owl:SymmetricProperty
- can add the following and have no need to state anything
owl:equivalentClass rdfs:subPropertyOf rdfs:subClassOf
owl:sameAs: Same Individuals
Suppose in 3 namespaces we have 3 different ways of describing a person
- how we can say that in all these 3 cases something/somebody is the same resource?
- e.g.
pr:WilliamShakspere owl:sameAs lit:Shakespeare
it’s defined by 3 rules: ```text only – when it’s a subject CONSTRUCT { ?s ?p ?x. } WHERE { ?s ?p ?y. ?x owl:sameAs ?y . }
– when it’s an object CONSTRUCT { ?x ?p ?o. } WHERE { ?y ?p ?o . ?x owl:sameAs ?y . }
– when it’s a predicate CONSTRUCT {?s ?x ?o. } WHERE { ?s ?y ?o . ?x owl:sameAs ?y . }
To avoid adding 3 more rules
- say that it's symmetric:
- <code>owl:sameAs rdf:type owl:SymmetricProperty</code>
## Sameness: Functional Properties
### <code>owl:FucntionalProperty</code>
Functional - of functions (in math)
- a property is functional if
- for some input value there could be only one output value
Examples (from RL):
- <code>hasMother</code> - can have only one biological mother
- <code>hasBirthplace</code>
- <code>birthdate</code>
In RDFS-plus use <code>owl:FucntionalProperty</code> to describe that
- a property can give only one value for one particular entry
```carbon
CONSTRUCT { ?a owl:sameAs ?b . }
WHERE {
?p rdf:type owl:FunctionalProperty .
?x ?p ?a .
?x ?p ?b .
}
Note the semantics
- if $x^2 = a \land x^2 = b \Rightarrow a = b$
- so if some resources participate in a functional property
- we conclude that these resources refer to the same entity (i.e. they are the same)
owl:InverseFunctionalProperty
Inverse of owl:FucntionalProperty
- a single value of an inverse functional property cannot be shared by two entities
- instead it infers that these two entities are the same
- and it doesn’t signalize any errors| |- examples: SSN, driver license, etc - anything that can be an ID number |
CONSTRUCT { ?a owl:sameAs ?b . } WHERE { ?p rdf:type owl:InverseFunctionalProperty . ?a ?p ?x . ?b ?p ?x . }
Examples
Student ID
- a student has an identity
- this ID # belongs only to one person
- so have this in the schema
:hasIdentityNo rdfs:domain :Student .:hasIdentityNo rdfs:range xsd:Integer .
- now ensure the uniqueness
:hasIdentityNo rdf:type owl:FunctionalProperty .:hasIdentityNo rdf:type owl:InverseFunctionalProperty .
Summary
Functional Only
hasMotherisa functional property only.- Someone has exactly one mother, but many people can share the same mother.
Inverse Functional Only
hasDiaryis an inverse functional property only- A person may have many diaries, but a diary is authored by one person only
Both Functional and Inverse Functional
- SSN, Student #, etc
Other Constructs
owl:DatatypeProperty and owl:ObjectPropery
In RDF, subjects and objects are resource
- they can be either another resources or some data items
Examples:
uni:studentId a owl:DatatypePropertybio:married a owl:ObjectProperty
owl:Class
owl:Class rdfs:subClassOf rdfs:Class .